Find the equivalent capacitance between the points A and B.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4 μF
Equivalent capacitance between A and B:
Top branch: two capacitors in series,
$C_{top}=\frac{3 \times 3}{3+3}=1.5 \,\mu F$
Bottom branch: two capacitors in series,
$C_{bottom}=\frac{3 \times 3}{3+3}=1.5 \,\mu F$
Diagonal capacitor (3 μF) parallel to left capacitor of top branch gives,
$C_{left}=3+3=6 \,\mu F$
So effective top branch,
$C_{top}=\frac{6 \times 3}{6+3}=\frac{18}{9}=2 \,\mu F$
Diagonal capacitor (3 μF) parallel to right capacitor of bottom branch gives,
$C_{right}=3+3=6 \,\mu F$
So effective bottom branch,
$C_{bottom}=\frac{3 \times 6}{3+6}=\frac{18}{9}=2 \,\mu F$
Now these two branches are in parallel,
$C_{eq}=2+2=4 \,\mu F$
Final Answer: $C_{eq}=4 \,\mu F$